Single draw from a 52-card deck. What is the probability that the card is either red or a king (count red kings only once)?

Introduction / Context:The event “red or king” requires inclusion–exclusion to avoid double-counting the red kings. Compute the probability in one draw from a standard deck.

Given Data / Assumptions:

• Red cards = 26 (hearts + diamonds).
• Kings = 4 total.
• Overlap (red kings) = 2 (K♥, K♦).

Concept / Approach:Use P(A ∪ B) = P(A) + P(B) − P(A ∩ B) with card counts.

Step-by-Step Solution:Count-based: favorable = 26 + 4 − 2 = 28.Probability = 28/52 = 7/13.

Verification / Alternative check:Fraction approach: 1/2 + 1/13 − 1/26 = 7/13.

Why Other Options Are Wrong:1/2 ignores kings of black suits; 6/13 or 27/52 misapply inclusion–exclusion; 5/13 undercounts.

Common Pitfalls:Double-counting red kings; forgetting there are two red suits.

Final Answer:7/13